Visualization of HARDI data

Visualization of HARDI data bmia.bmt.tue.nl/research/mviav Anna Vilanova a.vilanova @tue.nl

Introduction 26-10-2010 PAGE 1

What HARDI data? Diffusion Propagator P ( x ) Probability that a particle arrive to x given a fixed time. For each voxel we have a full probability density function. Diffusion Spectrum Imaging (a volume per voxel) 26-10-2010 PAGE 2

What HARDI data? Orientation Distribution Function O D F ( g) P ( rg) r d r 2 rg g rg g 0 Probability that a molecule is found in a given direction. is a unit vector. g g Fiber Orientation Distribution fo D F ( g ) Fraction of fiber portions in a given orientation within a voxel //Biomedical Engineering 26-10-2010 PAGE 3

Functions on the sphere Most of the HARDI models can be represented by functions on the sphere. (, ) ( g) w here g 1 Spherical Harmonics (SH) or Higher-Order Tensors (HOT) are used as representations. During this tutorial we will talk about one or the other, but remember that they represent the same and are interchangeable / Bimedical Engineering 26-10-2010 PAGE 4

Multi-Tensor Model Multi-Tensor Model does not use SH or HOT (Bergman et al. 2006) The weighted sum of k second-order tensors represent the signal /Biomedical Engineering 26-10-2010 PAGE 5

Visualizations Anisotropy Indices Glyphs Tractography 26-10-2010 PAGE 6

Anisotropy Indices (DTI) Based on eigenvalues of the tensor Most used quantities in clinic It is assumed that these indices give information about the quality of the underlying fibrous structure. FA /Biomedical Engineering 26-10-2010 PAGE 7

Anisotropy indices for HARDI Extended Anisotropy measures: Generalized Anisotropy (Ozarslan et al 2005 ), Generalized Fractional Anisotropy (Tuch 2004, Leow et al. 2008 ), Cumulative Residual Entropy (Rao et al. 2004, Chen et al. 2005 ), Fractional Multifiber Index (Frank 2002 ),R0,R2,Ri (Descoteaux 2006) M n ( g) ( g) n n d g d g 1 n Moments are used as anisotropy indices. M 2 is GFA Higher-order moments can also be used (Seunarine et al. 2009) Apply to different spherical diffusion functions ADC (Signal) Q-Ball, DOT, etc. /Biomedical Engineering 26-10-2010 PAGE 8

Anisotropy Indices for HARDI Reduce information to one scalar, easy to visualize Give an easy quantitative way to evaluate data They are not as widely used as DTI measures (FA) What extra information are they giving? (Prckovska et al 2008) This line of research is underdeveloped in HARDI literature. /Biomedical Engineering 26-10-2010 PAGE 9

Glyph Representation DTI Shows local information In 3D, clutter is a problem 1 e 1 (Kindlmann 2004) Ellipsoids Superquadrics e e 3 3 2 2 Cuboids /Biomedical Engineering 26-10-2010 PAGE 10

Glyph Representation HARDI HARDI information is more complex. What the Glyph represents depends on the model. DTI Ellipsoid Algebraic surfaces { x xd x ct} 2 /Biomedical Engineering 26-10-2010 PAGE 11

Glyph Representation HARDI Easy to build with DTI using eigenanalysis Not easy to generalize to HARDI due to the inverse General algebraic surfaces for second-order tensors (Strang 1998) DTI Ellipsoid General algebraic surfaces { x x D x ct} Generalisation (Qi 2006), maxima are minima. Contraintuitive T /Biomedical Engineering 26-10-2010 PAGE 12

Glyph Representation HARDI Spherical Polar Plots S ( g ) ( g ) g g 1 T S ( g ) ( g D g ) g S ( g ) ( g ) g /Biomedical Engineering 26-10-2010 PAGE 13

Maxima enhancement The maxima in (, ) are of interest Normalization is needed in most of the models QBall Normalized Showing arrows at maxima (Hlawitschka et al. 2005) Maxima enhancement by color coding XYZ - RGB color coding Distance to center based color coding (Hlawitschka et al. 2005) (Prckovska et al. 2010) /Biomedical Engineering 26-10-2010 PAGE 14

Maximum Enhancing Glyphs (Schultz et al 2009,Schultz et al 2010) Use the linear mapping defined by tensors DTI - It defines an Ellipsoid D S ( g ) D g D HARDI maxima enhancement glyphs (HOME) g 1 T tensor of order l S ( g ) T g T l 1 g 1 /Biomedical Engineering 26-10-2010 PAGE 15

Maximum Enhancing Glyphs HOME Glyphs Surface partition Color saturation modulation /Biomedical Engineering 26-10-2010 PAGE 16

Glyph s Rendering Polygonal meshes (Schultz et al. 2010): Simple Calculate geometry when changing seed points Accuracy depends on tessellation order Speed depends on tessellation order and amount of glyphs Ray-Casting for Spherical Harmonics: (Peeters et al. 2009, Almsick et al. 2010) Complex (GPU implementation) Quality depends on ray sampling steps Speed depends mainly on screen resolution, and number of glyphs. /Biomedical Engineering 26-10-2010 PAGE 17

Fiber population and multi-tensor glyphs Fiber population Spherical Deconvolution Maxima detection Multi-tensor model (Bergman et al 2006) (Schultz et al. 2008) /Biomedical Engineering 26-10-2010 PAGE 18

HARDI Tractography Deterministic HARDI Streamline Riemannian Framework Probabilistic Bayesian Bootstraping /Biomedical Engineering 26-10-2010 PAGE 19

HARDI Deterministic Tractography Extension of DTI streamlines Detection of Maxima Spherical Deconvolution ODF Multi-tensor model Interpolation Decide what fiber to follow 26-10-2010 PAGE 20 /Biomedical Engineering

HARDI Deterministic Tractography (Blyth et al. 2003 Hagmann et al 2007 Perrin et al. 2005 Jeurissen et al. 2010...) /Biomedical Engineering 26-10-2010 PAGE 21

HARDI Riemannian Framework DTI metric HARDI metric (Finsler) 1 G ( x ) D ( x ) G ( x, g ) f ( ( x, g )) [L. O Donnell et al. 02] [N.Wotawa et al. 05] (Melanakos et al. 2007) (Pichon et al 2005) /Biomedical Engineering 26-10-2010 PAGE 22

Probabilistic tractography :Bayesian p ( v D W d a ta, v ) p ( D W d a ta v ) p ( v v ) k k 1 k k k 1 Posterior Next step direction Given noise and previous direction Likelihood Models noise given a fiber orientaiton Prior Next direction given previous direction v k 1 (Friman et al. 2006 ) Cortesy of (CF Westin 2008) /Biomedical Engineering 26-10-2010 PAGE 23

Probabilistic tractography :Bayesian p ( v D W d a ta, v ) p ( D W d a ta v ) p ( v v ) k k 1 k k k 1 are used to randomly define the next step v k 1 Randomly trace thousand paths v k Challenge good estimation of the likelihood and prior (Parker et al 2003)(Cook et al. 2005-2006) (Seunarine et al. 2007) Courtesy of (CF Westin 2008) Log(probability of connection) /Biomedical Engineering 26-10-2010 PAGE 24

Probabilistic tractography :Bootstraping Resampling method : random sampling with replacement Measure in several directions and several times Random selection of perturbations of the directions and generate large number of datasets Calculate the variance of derived measures like Anisotropy indices, Eigenvalues, Eigenvectors, etc. Calculate the fibers generated from one seed point. (Haroon et al. 2007) (Berman et al. 2008) (Hosey et al. 2005) (Behrens et al 2007) (Jeurissen et al. 2010) /Biomedical Engineering 26-10-2010 PAGE 25

Hybrid Visualization Scheme (Prckovska et al. 2010) /Biomedical Engineering 26-10-2010 PAGE 26

Visualizations Scalar Indices Glyphs Tractography 26-10-2010 PAGE 27

Challenges Modeling (Signal Diffusion Fiber characteristics) Spliting, kissing fibers, diameter of fibers,... Identifying relevant quantitative measures (DTI FA) the visualization should consider this goal Information overload Interactive tools for visual data analysis (DSI, ODF, etc) Reduce memory and computational costs /Biomedical Engineering 26-10-2010 PAGE 28

Challenges Visual comparison between subjects Uncertainty estimation and visualization Mainly used in research environments What is the real value of HARDI? Validation /Biomedical Engineering 26-10-2010 PAGE 29

Acknowledgements Vesna Prckovska Paulo Rodrigues Neda Sepasian, Tim Peeters Ralph Brecheisen. Alard Roebroeck from Maastricht Brain Imaging Center Pim Pullens from Brain Innovation B.V., Maastricht Maxime Descoteaux from MOIVRE Centre for their valuable input and collaboration More information: bmia.bmt.tue.nl DTI Visualization Techniques and Applications

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